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- W2061734759 abstract "No non-trivial solutions are known of the diophantine equation f ( x , y )= f ( u , v ), where f ( x , y ) is the general quartic form given by f ( x , y )= ax 4 + bx 3 y + cx 2 y 2 + dxy 3 + ey 4 . This paper provides a necessary and sufficient condition for the existence of non-trivial solutions of this diophantine equation. It has also been shown that, using this condition, integer solutions of the equation f ( x , y )= f ( u , v ) can be obtained in specific cases. As an example, integer solutions have been obtained for the equation x 4 + x 3 y + x 2 y 2 + xy 3 + y 4 = u 4 + u 3 v + u 2 v 2 + uv 3 + v 4 ,which had not been solved earlier." @default.
- W2061734759 created "2016-06-24" @default.
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- W2061734759 date "1999-03-01" @default.
- W2061734759 modified "2023-09-28" @default.
- W2061734759 title "On the Quartic Diophantine Equationf(x,y)=f(u,v)" @default.
- W2061734759 cites W2082122984 @default.
- W2061734759 doi "https://doi.org/10.1006/jnth.1998.2322" @default.
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